9« 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1781. 



v, the original velocity of the bullet: Then 



is a theorem for finding the velocity on Mr. 



v = X 

 a 



— 4- - V 



bh ~ f * </Zh 



Robins's principles. 



v = - X TT +'~57 r - X v/'-j is the theorem proposed by Mr. Eider, who has 

 corrected a small error in Mr. Robins's method; and 



v = 5.672 eg s/f X —,-, — - is Dr. Hutton's theorem, which is sufficiently accu- 

 rate, and far more simple and expeditious than either of the preceding. It is to 

 be remembered, that g, h, and c, may be expressed in any measure; butf must 

 be English feet, and v will be the velocity of the bullet in English feet in a 

 second. 



The velocities of the bullets in most of the foregoing experiments were first 

 computed by Eider's method; but in going over the calculations a 2d time, Mr. 

 T. used Dr. Hutton's theorem. Both these methods gave the same velocity very 

 nearly, but the Doctor's method is by much the easiest in practice. In these 

 computations care was taken to make a proper allowance for the bullets that 

 were lodged in the pendulum, and also for the velocity lost by the bullet in pass- 

 ing through the screen. 



The corrections necessary on account of the bullets lodged in the pendulum 

 were made in the following manner. 



/; was continually added to the value of p, 



X b to the value of g, and 



f h 



- x b to the value of f 



Of the spaces occupied by the different charges of powder. — The heights of the 

 charges of powder, or the lengths of the spaces which they occupied in the bore, 

 were determined by measurement; and in order 

 that this might be done with greater accuracy, 

 inches and tenths of inches were marked on the 

 ram-rod, and the charge was gently forced down 

 till it occupied the same space in each experi- 

 ment. The annexed table shows the heights of 

 the charges as they were determined by mea- 

 surement, and also their heights computed from 

 the diameter of the bore of the piece, and the 

 specific gravity of the powder that was used. 



In the experiment N° 30, the powder was put into a cartridge so much 

 smaller than the bore of the piece, that the charge, instead of occupying I.45 

 inches, extended 3.2 inches. By this disposition of the powder, its action on 

 the bullet appears to have been very much diminished. 



h-> 



